用非线性规划证明最短置信区间存在性与唯一性

参数的区间估计是根据枢轴量的分布,在一定可靠度下指出被估计的总体参数所在的可能范围.衡量一个区间估计的优良性有两点,一是置信水平α(0<α<1),另一是区间的长度,通常的做法是对给定的置信水平α(如α=0.05或α=0.01)求出相应的置信区间,区间长度越短说明对参数的估计越准确.讨论了最短置信区间存在和唯一性以及最优置信区间的确定.

Discuss the Existence and the Uniqueness of the Shortest Confidence Interval According to the Nonlinear Programming

The interval estimation of parameter is a basic form for statistical conclusion,which can indicate the possible scale for estimated general parameter in a certain extent dependability based on the distribution of pivot quantity.The theory of Neyman confidence interval shows that the certain level of confidence ensures the certain extent dependability,but the precision is often scaled by the length of interval.In this article,according to the non-linear programming theory,both the existence and the uniquenes...